Betray Alliance

Betray Alliance is a dialogue option which allows you to transit back to the Disfavored path from the Rebel Path (only in Act I) or to the Anarchist path.

Overview
Narratively speaking, Betray Alliance (to start the Anarchist path) isn't so much the Fatebinder disagreeing with the associates they're following. Rather, it's expressing their desire to gain more personal power, with the implication that they can no longer do so on their current path.

As for the Rebel path, the Fatebinder has felt that they had enough of being part of Kyros's army, or that they are confident of subjugating the Tiers by relying on the locals instead of the help from either the Disfavored or the Scarlet Chorus.

Starting Rebel Path

 * During the Conquest, do NOT assassinate the Queen of Apex.
 * During the Conquest and Act I, earn as much favor with the Vendrien Guard as possible:
 * During the Conquest, become the Peacebinder.
 * During The Battle of Echocall Crossing, let both the villagers and VG (including Matani Sybil) escape.
 * During Taking the Outer Valley, let the VG (including Pelox Florian) escape.
 * During The Oathbreakers, agree to join the rebel cause.

While starting the Rebel path does not literally involve a "Betray Alliance" option, if you choose to falsely support Ashe, Barik will demand to speak to you outside the Disfavored camp. You can then use "Betray Alliance" to return to the Disfavored path. Note that in Act I, Barik is more opposed to supporting the rebels than Verse (although she too will lose some Loyalty along the way). In Act II, if you inform Barik that you are only using the rebels (Subterfuge check), his Loyalty will increase.

At Vendrien's Well Citadel, you'll eventually fight both the Chorus and the Disfavored. Also, unique to the Rebel path, there will be Vendrien Guardsmen in the citadel, not to mention the faction leaders who gather in Ascension Hall. Thus, a Betray Alliance on the Rebel path would mean fighting much closer to home compared to the other two paths.

Starting Anarchist Path

 * Before Act I ends, choose the option and fight against the faction you supported (Disfavored/Chorus/Rebels).

From Disfavored Path

 * Blade Grave: During That Which Remains, attacking Teodor after taking the Unbroken camp.
 * During Making a Stand, while talking to Rumalan.
 * Burning Library: Kill Maric during your first meeting with him.
 * Lethian's Crossing: If you left the Disfavored in charge of the Crossing, during Raetommon's attack on the Crossing (Iron and Blood).
 * When deciding Zdenya's fate during Forbidden Passage, killing her.
 * Stone Sea: During The Tiers Will Shake, while talking to Caedis and Radix, before learning of their plans for the region.
 * During Carving the Path, while talking to the Earthshaker guard at the entrance of the Earthshaker camp in Howling Rock.

From Chorus Path

 * Blade Grave: During A Broken Chord, attacking Jagged Remedy during your first meeting with him, before agreeing to recruit Mattias.
 * Doing so allows you to skip Duskwatch Fort and Rust Canyons, as the Chorus led you straight to Mattias and Irentis, allowing you to retrieve Dauntless and the Steadfast Insignia.
 * Burning Library: During The Silence of Secrets, while talking to The Censor, before joining the "hunt".
 * Lethian's Crossing: If you left the Chorus in charge of the Crossing, during Raetommon's attack on the Crossing (Blood and Bronze).
 * When deciding Zdenya's fate during Finding a Madman, killing her.
 * Stone Sea: Multiple opportunities. However, note the main objective of the Anarchist path in the region: recovering the Azure Shield. It is possible to become stuck due to Red-Fang not responding to you.
 * In the Anarchist Path, the only way to end the Edict of Stone is to wage war against the Earthshakers, specifically by killing Basilon first for the Shard of Pure Azurelith, before storming the Earthshaker compound at Howling Rock.

From Rebel Path

 * Lethian's Crossing: During Crossing the Oldwalls, kill Zdenya and attack Welby.
 * Blade Grave: During Battered but Unbroken, attack Captain Agathon.
 * During A Daunting Path, attack while talking to the Unbroken guard at the entrance of the camp, or while talking to Mattias inside the camp.
 * During That Which Remains, while talking to Elia.
 * During Making a Stand, while confronting Amelia.
 * Burning Library: During Heated Words, attack Renata.
 * Stone Sea: Note that whatever your actions in the region, the critical aspect is to secure the Azure Shield from Red-Fang. If not, you may not get another chance to talk to/fight her, preventing progression should you go Anarchist. Notably, you cannot acquire the Shield if your allies in the Stone Sea are the Stonestalkers.

Act III Betray Alliance
If you complete The Third Degree in the Disfavored path by having Nerat consume Verse, you will receive the ending slides for the Anarchist path instead.